Abstract: Recent studies indicate that measurements of fractal and multifractal
parameters of active regions (ARs) are not efficient tools to discriminate ARs
on the basis of the flare activity, as well as to predict flare events.
Attempting validation of this result on a large data set of higher spatial and
temporal resolution, as well as higher flux sensitivity, observations than
employed in previous studies, we analyzed high-cadence time series of
line-of-sight magnetograms of 43 ARs characterized by different flare activity,
which were observed with SDO/HMI from May 2010 to December 2013. On these data,
we estimated four parameters, the generalized fractal dimensions $D_0$ and
$D_8$, and the multifractal parameters $C_{\mathrm{div}}$ and
$D_{\mathrm{div}}$. We found distinct average values of the parameters measured
on ARs that have hosted flares of different class. However, the dispersion of
values measured on ARs that have produced same class events is such that the
parameters deduced from distinct classes of flaring regions can also largely
overlap. Based on the results of our measurements, C- and M-class flaring ARs
are practically indistinguishable, as well as M- and X-class flaring ARs. We
found consistent changes on the time series of the measured parameters only on
$\approx$ 50\% of the studied ARs and $\approx$ 50\% of the M- and X-class
events considered. We show that these results hold for fractal and multifractal
parameter estimates based on both total unsigned and signed flux data of the
analyzed ARs.